Final answer:
We calculate the probability of a student being male (5/9) and female (4/9). The least number of students in the group that would allow us to compute this fraction of right-handed female students is 41 when rounded up to the least integer.
Step-by-step explanation:
The question requires us to calculate the probabilities of a student being male (P(M)) and a student being female (P(F)). To solve this, we can use the given information that 5/9 of the students are male, which means 4/9 must be female. Since the total probabilities of all possibilities must equal 1, P(M) = 5/9 implies that P(F) = 1 - P(M) = 1 - 5/9 = 4/9.
Next, we know that 5/6 of the female students are right-handed. To find the least integer value, we need a scenario where the number of female students is divisible by both 9 (from the fraction 4/9) and 6 (from the fraction 5/6). The least common multiple (LCM) of 6 and 9 is 18, so the least integer number of students in the group that would allow us to compute the fraction of right-handed female students is 18 females. Since this represents the entire group of female students, the total number of students in the group would be (18/4) * 9 = 40.5, which we round up to the least integer value, 41.